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Identical expressions
(arctg(two x))/(pi(one +4x^2))
(arctg(2x)) divide by ( Pi (1 plus 4x squared ))
(arctg(two x)) divide by ( Pi (one plus 4x squared ))
(arctg(2x))/(pi(1+4x2))
arctg2x/pi1+4x2
(arctg(2x))/(pi(1+4x²))
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arctg2x/pi1+4x^2
(arctg(2x)) divide by (pi(1+4x^2))
(arctg(2x))/(pi(1+4x^2))dx
Similar expressions
(arctg(2x))/(pi(1-4x^2))

Solving integrals/ (arctg(2x))/(pi(1+4x^2))

Integral of (arctg(2x))/(pi(1+4x^2)) dx

The solution

You have entered [src]

 oo                 
  /                 
 |                  
 |    atan(2*x)     
 |  ------------- dx
 |     /       2\   
 |  pi*\1 + 4*x /   
 |                  
/                   
0

$$\int\limits_{0}^{\infty} \frac{\operatorname{atan}{\left(2 x \right)}}{\pi \left(4 x^{2} + 1\right)}\, dx$$

Integral(atan(2*x)/((pi*(1 + 4*x^2))), (x, 0, oo))

The answer (Indefinite) [src]

  /                                 
 |                            2     
 |   atan(2*x)            atan (2*x)
 | ------------- dx = C + ----------
 |    /       2\             4*pi   
 | pi*\1 + 4*x /                    
 |                                  
/

$$\int \frac{\operatorname{atan}{\left(2 x \right)}}{\pi \left(4 x^{2} + 1\right)}\, dx = C + \frac{\operatorname{atan}^{2}{\left(2 x \right)}}{4 \pi}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi
--
16

$$\frac{\pi}{16}$$

pi
--
16

$$\frac{\pi}{16}$$

pi/16

Use the examples entering the upper and lower limits of integration.

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Integral of (arctg(2x))/(pi(1+4x^2)) dx

Limits of integration:

The graph:

Piecewise:

The solution